A simple method for calculating heat transfer from a rotating disk to fluids for a wide range of Prandtl numbers using asymptotic analysis is presented. Nusselt numbers for a heated rotating disk for different Prandtl numbers is expressed in terms of the asymptotic Nusselt numbers corresponding to a very small value of Prandtl numbers and Nusselt numbers corresponding to a very large value of Prandtl numbers. The proposed model uses a concave downward asymptotic correlation method to develop a robust compact model. Using the methods discussed by Churchill and Usagi (1972, “General Expression for the Correlation of Rates of Transfer and Other Phenomena,” AIChE J., 18(6), pp. 1121–1128), the fitting parameter in the proposed model can be determined at Prandtl numbers corresponding to the intersection of the two asymptotes.
Issue Section:
Technical Briefs
1.
von Kármán
, Th.
, 1921, “Über Laminare und Turbulente Reibung
,” ZAMM
0044-2267, 1
, pp. 233
–252
.2.
Cochran
, W. G.
, 1934, “The Flow Due to a Rotating Disk
,” Proc. Cambridge Philos. Soc.
0068-6735, 30
, pp. 365
–375
.3.
Hannah
, D. M.
, 1947, “Forced Flow Against a Rotating Disk
,” British A. R. C. Report and Memo. No. 2772.4.
Ostrach
, S.
, and Thornton
, P. R.
, 1958, “Compressible Laminar Flow and Heat Transfer About a Rotating Isothermal Disk
,” NACA Report No. TN 4320.5.
Wanger
, C.
, 1948, “Heat Transfer From a Rotating Disk to Ambient Air
,” J. Appl. Phys.
0021-8979, 19
(9
), pp. 837
–839
.6.
Millsap
, K.
, and Pohlhausen
, K.
, 1952, “Heat Transfer by Laminar Flow From a Rotating Plate
,” J. Aeronaut. Sci.
0095-9812, 19
(2
), pp. 120
–126
.7.
Cobb
, E. C.
, and Saunders
, O. A.
, 1956, “Heat Transfer From a Rotating Disk
,” Proc. R. Soc. London, Ser. A
1364-5021, 236
, (1205
), pp. 343
–351
.8.
Kreith
, F.
, Taylor
, J. H.
, and Chang
, J. P.
, 1959, “Heat and Mass Transfer From a Rotating Disk
,” ASME J. Heat Transfer
0022-1481, 81
, pp. 95
–105
.9.
Sparrow
, E. M.
, and Gregg
, J. L.
, 1959, “Heat Transfer From a Rotating Disk to Fluids at Any Prandtl Number
,” ASME J. Heat Transfer
0022-1481, 81
, pp. 249
–251
.10.
Hartnett
, J. P.
, 1959, “Heat Transfer From a Non-Isothermal Disk Rotating in Still Air
,” ASME J. Appl. Mech.
0021-8936, 81
, pp. 672
–673
.11.
Hartnett
, J. P.
, and Deland
, E. C.
, 1961, “The Influence of Prandtl Number on the Heat Transfer From Rotating Nonisothermal Disks and Cones
,” ASME J. Heat Transfer
0022-1481, 83
, pp. 95
–96
.12.
Mabuchi
, I.
, Tanaka
, T.
, and Sakakibara
, Y.
, 1967, “Studies on the Convective Heat Transfer From Rotating Disk (2nd Report, The Effect of Prandtl Number on the Laminar Heat Transfer From a Disk Rotating in Uniform Forced Stream)
,” Bull. JSME
0021-3764, 10
(42
), pp. 965
–974
.13.
Sano
, T.
, 1973, “A Note on Asymptotic Solutions for Heat Transfer in Laminar Forced Flow Against a Non-Isothermal Rotating Disk
,” Waerme- Stoffuebertrag.
0042-9929/Thermo- and Fluid Dynamics, 6
(2
), pp. 108
–113
.14.
Popiel
, Cz. O.
, , and Boguslawski
, L.
, 1975, “Local Heat-Transfer Coefficients on the Rotating Disk in Still Air
,” Int. J. Heat Mass Transfer
0017-9310, 18
(1
), pp. 167
–170
.15.
Oehlbeck
, D. L.
, and Erian
, F. F.
, 1979, “Heat Transfer From Axisymmetric Sources at the Surface of a Rotating Disk
,” Int. J. Heat Mass Transfer
0017-9310, 22
(4
), pp. 601
–610
.16.
Muir
, P. H.
, Fairweather
, G.
, and Vedha-Nayagam
, M.
, 1983, “Effect of Prandtl Number on Heat Transfer From an Isothermal Rotating Disk With Blowing at the Wall
,” Int. Commun. Heat Mass Transfer
0735-1933, 10
(4
), pp. 287
–297
.17.
Lin
, H. T.
, and Lin
, L. K.
, 1987, “Heat Transfer From a Rotating Cone or Disk to Fluids of Any Prandtl Number
,” Int. Commun. Heat Mass Transfer
0735-1933, 14
(3
), pp. 323
–332
.18.
Wang
, T. -Y.
, and Kleinstreuer
, C.
, 1990, “Similarity Solution of Combined Convection Heat Transfer From a Rotating Cone or Disk to Non-Newtonian Fluids
,” ASME J. Heat Transfer
0022-1481, 112
(4
), pp. 939
–944
.19.
Weigand
, B.
, 2004, Analytical Methods for Heat Transfer and Fluid Flow Problems
, Springer
, New York
, Chap. 6.20.
Churchill
, S. W.
, and Usagi
, R.
, 1972, “A General Expression for the Correlation of Rates of Transfer and Other Phenomena
,” AIChE J.
0001-1541, 18
(6
), pp. 1121
–1128
.21.
Churchill
, S. W.
, 1988, Viscous Flows: The Practical Use of Theory
, Butterworths
, Boston, MA
.22.
Kraus
, A. D.
, and Bar-Cohen
, A.
, 1983, Thermal Analysis and Control of Electronic Equipment
, Hemisphere
, New York
.23.
Yovanovich
, M. M.
, 2003, “Asymptotes and Asymptotic Analysis for Development of Compact Models for Microelectronic Cooling
,” 19th Annual Semiconductor Thermal Measurement and Management Symposium and Exposition (SEMI-THERM), San Jose, CA.Copyright © 2008
by American Society of Mechanical Engineers
You do not currently have access to this content.
